We analyze $f$-frequently hypercyclic, $q$-frequently hypercyclic ($q> 1$) and frequently hypercyclic $C_{0}$-semigroups ($q=1$) defined on complex sectors, working in the setting of separable infinite-dimensional Fr\'echet spaces. Some structural results of ours are given for a general class of ${\mathcal F}$-frequently hypercyclic $C_{0}$-semigroups, as well. We investigate generalized frequently hypercyclic translation semigroups and generalized frequently hypercyclic semigroups induced by semiflows on weighted function spaces. Several illustrative examples are presented.

中文翻译：

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f-频繁超循环 $$C_{0}$$C0-复杂扇区上的半群

我们分析了在复杂扇区上定义的 $f$-频繁超循环、$q$-频繁超循环 ($q> 1$) 和频繁超循环 $C_{0}$-semigroups ($q=1$)，工作在可分离的无限维 Fr\'echet 空间。我们的一些结构结果也适用于 ${\mathcal F}$-频繁超循环 $C_{0}$-半群的一般类。我们研究了加权函数空间上的半流引起的广义频繁超循环平移半群和广义频繁超循环半群。提供了几个说明性示例。